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Teachers & SchoolsMathematical Reasoning Drill 5, Problem 1. Which of the following could be the number of pieces the lasagna was cut into?

CAHSEE Math | Mathematical Reasoning |

Language | English Language |

Logic and Proofs | Algebraic Proof |

Mathematical Reasoning | Formulating conjectures |

If two of Jon’s friends were to come over and five people were to share it,

two pieces would be left over… …and if nine people were to share it,

three pieces would be left over.

Which of the following could be the number of pieces the lasagna was cut into?

And here are the potential answers…

At first, this problem looks really hard.

We need to find a number that has no remainder when we divide it by three…

...a remainder of two when we divide it by five,

and a remainder of three when we divide it by nine.

Lucky for us, this question is multiple choice…

…which means all we have to do is test the answer choices, starting with (A).

If we divide (A) by three, we get twelve divided by three is four, with no remainder.

Good so far.

Twelve divided by five is two, with a remainder of two.

That’s also what we want, so this looks promising.

Twelve divided by nine is one, with a remainder of three.

Great! This is our answer. And lucky us, we got it on the first try.

It’s usually a good idea to make sure though,

so let’s check out the other answers and try to see why they’re wrong.

The problem with (B) is that twenty-one divided by five is four with a remainder of one, not two.

With (C), thirty divided by five leaves a remainder of zero,

which also isn’t what we’re looking for.

We get a similar problem with (D): thirty-nine divided by five has a remainder of four.

Looks like our answer is (A).

As in, “All gone.”